How to Simplify Fractions Step by Step
A clear, repeatable process to reduce any fraction and avoid common mistakes.
Simplifying fractions means reducing a fraction to its smallest, most efficient form without changing its value. This skill shows up in algebra, geometry, and real-life math, so it is worth mastering.
If you want to check your work fast, use the Fraction Simplifier tool.
Quick Takeaways
- Find the greatest common factor (GCF) of the numerator and denominator.
- Divide both by the same number until no common factors remain.
- Always keep the value the same while reducing the numbers.
"Simplifying does not change the fraction's value, it only makes it simpler to read and use."
Step-by-Step: Simplify Any Fraction
Step 1: Find the GCF
The GCF is the largest number that divides both the numerator and denominator.
Example: Simplify 24/36
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
GCF = 12
Step 2: Divide Both by the GCF
24/36 = (24 ÷ 12) / (36 ÷ 12) = 2/3
Step 3: Double-Check
Make sure there is no larger common factor left.
2 and 3 share no common factors, so 2/3 is fully simplified.
Alternate Method: Prime Factorization
If the GCF is not obvious, break both numbers into prime factors.
Example: Simplify 18/30
18 = 2 × 3 × 3
30 = 2 × 3 × 5
Cancel the common factors (2 and 3): 18/30 = 3/5
Quick Practice Table
| Original fraction | GCF | Simplified fraction |
|---|---|---|
| 12/16 | 4 | 3/4 |
| 15/25 | 5 | 3/5 |
| 42/56 | 14 | 3/4 |
| 63/81 | 9 | 7/9 |
Common Mistakes to Avoid
| Mistake | Why it is wrong | Fix |
|---|---|---|
| Dividing only the top or bottom | Changes the value of the fraction | Always divide both by the same number |
| Canceling numbers that are not factors | Gives the wrong result | Only cancel common factors |
| Stopping too early | Fraction is not fully reduced | Keep going until the GCF is 1 |
Simplifying Mixed Numbers and Improper Fractions
- Improper fractions: Simplify the fraction part directly.
Example:45/60 = 3/4 - Mixed numbers: Convert to an improper fraction first, simplify, then convert back if needed.
Example:2 6/8 = 2 3/4
A Simple Check
Multiply the simplified fraction by the GCF you used.
If it returns the original numerator and denominator, you are good.
Final Thoughts
Simplifying fractions is a small skill with big impact. Once you can spot common factors quickly, the process becomes fast and reliable. If you want instant feedback, try the Fraction Simplifier and compare it with your steps.